Regression Models MA data analysis
Additive Multiple Linear Model
solid and liquid food waste
## Response food_waste_kg :
##
## Call:
## lm(formula = food_waste_kg ~ var., data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.9444 -0.6870 -0.1213 0.5307 3.2825
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.4487861 0.7001179 -2.069 0.0403 *
## var.temp_c 0.0028126 0.0086899 0.324 0.7466
## var.humi_p 0.0053388 0.0073629 0.725 0.4695
## var.prcp_mm -0.0417248 0.0396404 -1.053 0.2942
## var.tueE 0.1706132 0.1857893 0.918 0.3599
## var.wedE -0.1088752 0.1849244 -0.589 0.5569
## var.thuE -0.3865671 0.1787284 -2.163 0.0322 *
## var.friE 0.1925727 0.1752651 1.099 0.2737
## var.satE -0.2594445 0.1845003 -1.406 0.1618
## var.container 0.2795788 0.1621429 1.724 0.0867 .
## var.liquors 0.0060825 0.0523540 0.116 0.9077
## var.sales 0.0039416 0.0005678 6.942 1.13e-10 ***
## var.halfs 0.0691157 0.0283383 2.439 0.0159 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9858 on 148 degrees of freedom
## Multiple R-squared: 0.543, Adjusted R-squared: 0.506
## F-statistic: 14.66 on 12 and 148 DF, p-value: < 2.2e-16
##
##
## Response solid_waste_kg :
##
## Call:
## lm(formula = solid_waste_kg ~ var., data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.77317 -0.26285 -0.08542 0.17375 2.23890
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.3393464 0.2891174 -1.174 0.2424
## var.temp_c -0.0018981 0.0035885 -0.529 0.5976
## var.humi_p 0.0010506 0.0030406 0.346 0.7302
## var.prcp_mm -0.0173666 0.0163697 -1.061 0.2905
## var.tueE 0.1472586 0.0767227 1.919 0.0569 .
## var.wedE -0.0170184 0.0763655 -0.223 0.8240
## var.thuE -0.1422127 0.0738068 -1.927 0.0559 .
## var.friE 0.0577250 0.0723767 0.798 0.4264
## var.satE -0.0972288 0.0761904 -1.276 0.2039
## var.container -0.0292830 0.0669578 -0.437 0.6625
## var.liquors 0.0078168 0.0216199 0.362 0.7182
## var.sales 0.0012807 0.0002345 5.462 1.94e-07 ***
## var.halfs 0.0138583 0.0117024 1.184 0.2382
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4071 on 148 degrees of freedom
## Multiple R-squared: 0.3845, Adjusted R-squared: 0.3346
## F-statistic: 7.704 on 12 and 148 DF, p-value: 5.36e-11
##
##
## Response liquid_waste_kg :
##
## Call:
## lm(formula = liquid_waste_kg ~ var., data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.42750 -0.48344 -0.07879 0.44523 1.80789
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.1094396 0.4911865 -2.259 0.02536 *
## var.temp_c 0.0047107 0.0060966 0.773 0.44095
## var.humi_p 0.0042882 0.0051656 0.830 0.40780
## var.prcp_mm -0.0243582 0.0278108 -0.876 0.38253
## var.tueE 0.0233546 0.1303455 0.179 0.85805
## var.wedE -0.0918567 0.1297387 -0.708 0.48005
## var.thuE -0.2443544 0.1253917 -1.949 0.05322 .
## var.friE 0.1348477 0.1229620 1.097 0.27457
## var.satE -0.1622157 0.1294412 -1.253 0.21211
## var.container 0.3088618 0.1137557 2.715 0.00741 **
## var.liquors -0.0017344 0.0367304 -0.047 0.96240
## var.sales 0.0026609 0.0003983 6.680 4.52e-10 ***
## var.halfs 0.0552573 0.0198815 2.779 0.00615 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6916 on 148 degrees of freedom
## Multiple R-squared: 0.5535, Adjusted R-squared: 0.5173
## F-statistic: 15.29 on 12 and 148 DF, p-value: < 2.2e-16Coefficients Visualization
Per Customer
## Response food_waste_p_kg :
##
## Call:
## lm(formula = food_waste_p_kg ~ var., data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.070808 -0.025440 -0.002235 0.020112 0.146466
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.970e-02 2.660e-02 1.492 0.138
## var.temp_c 1.395e-04 3.301e-04 0.423 0.673
## var.humi_p 5.093e-05 2.797e-04 0.182 0.856
## var.prcp_mm -1.914e-03 1.506e-03 -1.271 0.206
## var.tueE 5.465e-03 7.058e-03 0.774 0.440
## var.wedE -6.143e-03 7.025e-03 -0.874 0.383
## var.thuE -7.898e-03 6.790e-03 -1.163 0.247
## var.friE 8.833e-03 6.658e-03 1.327 0.187
## var.satE -1.050e-02 7.009e-03 -1.499 0.136
## var.container 1.533e-02 6.160e-03 2.488 0.014 *
## var.liquors 1.945e-03 1.989e-03 0.978 0.330
## var.sales 3.475e-05 2.157e-05 1.611 0.109
## var.halfs 6.672e-04 1.077e-03 0.620 0.536
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03745 on 148 degrees of freedom
## Multiple R-squared: 0.1602, Adjusted R-squared: 0.09214
## F-statistic: 2.353 on 12 and 148 DF, p-value: 0.008537
##
##
## Response solid_waste_p_kg :
##
## Call:
## lm(formula = solid_waste_p_kg ~ var., data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.027111 -0.009757 -0.001349 0.007366 0.101048
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.035e-02 1.107e-02 1.838 0.0680 .
## var.temp_c -4.721e-05 1.374e-04 -0.344 0.7316
## var.humi_p -3.825e-05 1.164e-04 -0.329 0.7430
## var.prcp_mm -8.164e-04 6.267e-04 -1.303 0.1947
## var.tueE 5.960e-03 2.937e-03 2.029 0.0442 *
## var.wedE -2.923e-04 2.924e-03 -0.100 0.9205
## var.thuE -3.814e-03 2.826e-03 -1.350 0.1792
## var.friE 1.786e-03 2.771e-03 0.645 0.5202
## var.satE -3.992e-03 2.917e-03 -1.368 0.1732
## var.container -9.782e-05 2.563e-03 -0.038 0.9696
## var.liquors 6.219e-04 8.277e-04 0.751 0.4537
## var.sales 1.336e-05 8.976e-06 1.489 0.1387
## var.halfs -2.354e-04 4.480e-04 -0.525 0.6001
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01559 on 148 degrees of freedom
## Multiple R-squared: 0.09039, Adjusted R-squared: 0.01664
## F-statistic: 1.226 on 12 and 148 DF, p-value: 0.2707
##
##
## Response liquid_waste_p_kg :
##
## Call:
## lm(formula = liquid_waste_p_kg ~ var., data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.04658 -0.01829 -0.00111 0.01530 0.07904
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.935e-02 1.875e-02 1.032 0.303893
## var.temp_c 1.867e-04 2.328e-04 0.802 0.423722
## var.humi_p 8.918e-05 1.972e-04 0.452 0.651806
## var.prcp_mm -1.098e-03 1.062e-03 -1.034 0.302856
## var.tueE -4.951e-04 4.977e-03 -0.099 0.920881
## var.wedE -5.851e-03 4.953e-03 -1.181 0.239422
## var.thuE -4.084e-03 4.787e-03 -0.853 0.394946
## var.friE 7.047e-03 4.695e-03 1.501 0.135461
## var.satE -6.512e-03 4.942e-03 -1.318 0.189633
## var.container 1.542e-02 4.343e-03 3.551 0.000515 ***
## var.liquors 1.323e-03 1.402e-03 0.943 0.347015
## var.sales 2.139e-05 1.521e-05 1.406 0.161732
## var.halfs 9.026e-04 7.591e-04 1.189 0.236315
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02641 on 148 degrees of freedom
## Multiple R-squared: 0.209, Adjusted R-squared: 0.1449
## F-statistic: 3.26 on 12 and 148 DF, p-value: 0.0003427Coefficients Visualization
## Warning: `aes_string()` was deprecated in ggplot2 3.0.0.
## ℹ Please use tidy evaluation idioms with `aes()`.
## ℹ See also `vignette("ggplot2-in-packages")` for more information.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
RDiT
Day of the week plot
Scatter plot
## Scatter plot per Customer
RDinT Analysis
Interaction
## Response food_waste_kg :
##
## Call:
## lm(formula = food_waste_kg ~ var., data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.3728 -1.0750 -0.1146 0.7660 3.9877
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.640999 0.303450 5.408 2.34e-07 ***
## var.container 0.451440 0.440216 1.025 0.3067
## var.time -0.013091 0.006059 -2.161 0.0322 *
## var. 0.014899 0.009594 1.553 0.1225
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.395 on 157 degrees of freedom
## Multiple R-squared: 0.02956, Adjusted R-squared: 0.01101
## F-statistic: 1.594 on 3 and 157 DF, p-value: 0.1931
##
##
## Response solid_waste_kg :
##
## Call:
## lm(formula = solid_waste_kg ~ var., data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7752 -0.3082 -0.1020 0.2648 2.1840
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.627004 0.107778 5.818 3.25e-08 ***
## var.container 0.002645 0.156354 0.017 0.987
## var.time -0.003309 0.002152 -1.538 0.126
## var. 0.003462 0.003408 1.016 0.311
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4954 on 157 degrees of freedom
## Multiple R-squared: 0.03307, Adjusted R-squared: 0.01459
## F-statistic: 1.79 on 3 and 157 DF, p-value: 0.1514
##
##
## Response liquid_waste_kg :
##
## Call:
## lm(formula = liquid_waste_kg ~ var., data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.59768 -0.82269 -0.00855 0.56427 2.82840
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.013995 0.214848 4.720 5.19e-06 ***
## var.container 0.448795 0.311680 1.440 0.1519
## var.time -0.009783 0.004290 -2.280 0.0239 *
## var. 0.011437 0.006793 1.684 0.0942 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9875 on 157 degrees of freedom
## Multiple R-squared: 0.03439, Adjusted R-squared: 0.01594
## F-statistic: 1.864 on 3 and 157 DF, p-value: 0.1379##
## Call:
## lm(formula = rdt_int_fw, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.3728 -1.0750 -0.1146 0.7660 3.9877
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.640999 0.303450 5.408 2.34e-07 ***
## container 0.451440 0.440216 1.025 0.3067
## time -0.013091 0.006059 -2.161 0.0322 *
## container:time 0.014899 0.009594 1.553 0.1225
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.395 on 157 degrees of freedom
## Multiple R-squared: 0.02956, Adjusted R-squared: 0.01101
## F-statistic: 1.594 on 3 and 157 DF, p-value: 0.1931##
## Call:
## lm(formula = rdt_int_sfw, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.7752 -0.3082 -0.1020 0.2648 2.1840
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.627004 0.107778 5.818 3.25e-08 ***
## container 0.002645 0.156354 0.017 0.987
## time -0.003309 0.002152 -1.538 0.126
## container:time 0.003462 0.003408 1.016 0.311
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4954 on 157 degrees of freedom
## Multiple R-squared: 0.03307, Adjusted R-squared: 0.01459
## F-statistic: 1.79 on 3 and 157 DF, p-value: 0.1514##
## Call:
## lm(formula = rdt_int_lfw, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.59768 -0.82269 -0.00855 0.56427 2.82840
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.013995 0.214848 4.720 5.19e-06 ***
## container 0.448795 0.311680 1.440 0.1519
## time -0.009783 0.004290 -2.280 0.0239 *
## container:time 0.011437 0.006793 1.684 0.0942 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9875 on 157 degrees of freedom
## Multiple R-squared: 0.03439, Adjusted R-squared: 0.01594
## F-statistic: 1.864 on 3 and 157 DF, p-value: 0.1379Ass-Interaction
- Linearity of the relationships between the dependent and independent variables
- Normality of the residuals
- Homoscedasticity of the residuals
- No influential points (outliers)
- No multicollinearity
- Independence of the observations
## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.006).## Warning: Heteroscedasticity (non-constant error variance) detected (p < .001).## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.023).## Warning: Non-normality of residuals detected (p < .001).## Warning: Non-normality of residuals detected (p < .001).## Warning: Non-normality of residuals detected (p < .001).##
## studentized Breusch-Pagan test
##
## data: rdt_int_fw
## BP = 7.8124, df = 3, p-value = 0.05005##
## studentized Breusch-Pagan test
##
## data: rdt_int_sfw
## BP = 5.4746, df = 3, p-value = 0.1402##
## studentized Breusch-Pagan test
##
## data: rdt_int_lfw
## BP = 7.3214, df = 3, p-value = 0.06233## OK: Residuals appear to be independent and not autocorrelated (p = 0.486).## OK: Residuals appear to be independent and not autocorrelated (p = 0.536).## OK: Residuals appear to be independent and not autocorrelated (p = 0.484).
Multiple model
##
## Call:
## lm(formula = rdt_multi_fw, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.0485 -0.6500 -0.0912 0.4476 3.3391
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.2312704 0.9452769 -2.360 0.0195 *
## container 0.5782882 0.3674976 1.574 0.1177
## time -0.0083069 0.0065926 -1.260 0.2096
## temp_c -0.0105319 0.0126725 -0.831 0.4072
## humi_p 0.0091364 0.0093094 0.981 0.3280
## prcp_mm -0.0393178 0.0405061 -0.971 0.3333
## liquors -0.0103638 0.0509853 -0.203 0.8392
## sales 0.0040949 0.0005081 8.059 2.17e-13 ***
## halfs 0.0715002 0.0294293 2.430 0.0163 *
## container:time 0.0093167 0.0100585 0.926 0.3558
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.008 on 151 degrees of freedom
## Multiple R-squared: 0.5122, Adjusted R-squared: 0.4832
## F-statistic: 17.62 on 9 and 151 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = rdt_multi_sfw, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.67954 -0.25736 -0.07937 0.18700 2.32548
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.4376693 0.3876971 -1.129 0.261
## container 0.1019002 0.1507259 0.676 0.500
## time -0.0025510 0.0027039 -0.943 0.347
## temp_c -0.0056240 0.0051975 -1.082 0.281
## humi_p 0.0014782 0.0038182 0.387 0.699
## prcp_mm -0.0154605 0.0166132 -0.931 0.354
## liquors 0.0080184 0.0209112 0.383 0.702
## sales 0.0012142 0.0002084 5.826 3.31e-08 ***
## halfs 0.0130254 0.0120702 1.079 0.282
## container:time 0.0016192 0.0041254 0.392 0.695
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4135 on 151 degrees of freedom
## Multiple R-squared: 0.3519, Adjusted R-squared: 0.3133
## F-statistic: 9.112 on 9 and 151 DF, p-value: 5.999e-11##
## Call:
## lm(formula = rdt_multi_lfw, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.55792 -0.44014 -0.07213 0.38966 1.87255
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.7936011 0.6627069 -2.706 0.00758 **
## container 0.4763880 0.2576422 1.849 0.06641 .
## time -0.0057559 0.0046219 -1.245 0.21493
## temp_c -0.0049079 0.0088843 -0.552 0.58148
## humi_p 0.0076581 0.0065265 1.173 0.24249
## prcp_mm -0.0238573 0.0283977 -0.840 0.40217
## liquors -0.0183822 0.0357444 -0.514 0.60782
## sales 0.0028807 0.0003562 8.086 1.85e-13 ***
## halfs 0.0584748 0.0206321 2.834 0.00522 **
## container:time 0.0076975 0.0070517 1.092 0.27676
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7069 on 151 degrees of freedom
## Multiple R-squared: 0.5242, Adjusted R-squared: 0.4958
## F-statistic: 18.48 on 9 and 151 DF, p-value: < 2.2e-16Ass-Multiple
- Linearity of the relationships between the dependent and independent variables
- Normality of the residuals
- Homoscedasticity of the residuals
- No influential points (outliers)
- No multicollinearity
- Independence of the observations
## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.008).## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.006).## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.003).## Warning: Non-normality of residuals detected (p = 0.001).## Warning: Non-normality of residuals detected (p < .001).## Warning: Non-normality of residuals detected (p = 0.023).##
## studentized Breusch-Pagan test
##
## data: rdt_multi_fw
## BP = 14.705, df = 9, p-value = 0.09935##
## studentized Breusch-Pagan test
##
## data: rdt_multi_sfw
## BP = 10.062, df = 9, p-value = 0.3455##
## studentized Breusch-Pagan test
##
## data: rdt_multi_lfw
## BP = 15.294, df = 9, p-value = 0.08316## OK: Residuals appear to be independent and not autocorrelated (p = 0.526).## OK: Residuals appear to be independent and not autocorrelated (p = 0.524).## OK: Residuals appear to be independent and not autocorrelated (p = 0.448).
Polynomial model
##
## Call:
## lm(formula = rdt_poly_fw, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.0072 -0.6418 -0.1261 0.4642 3.2952
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.4671604 1.0125798 -2.437 0.0160 *
## container 0.3838594 0.5208439 0.737 0.4623
## time -0.0189069 0.0186297 -1.015 0.3118
## I(time^2) -0.0001330 0.0002020 -0.658 0.5114
## temp_c -0.0083476 0.0127768 -0.653 0.5145
## humi_p 0.0103180 0.0093920 1.099 0.2737
## prcp_mm -0.0513615 0.0414043 -1.240 0.2167
## liquors -0.0068301 0.0510638 -0.134 0.8938
## sales 0.0041346 0.0005102 8.104 1.78e-13 ***
## halfs 0.0703055 0.0296094 2.374 0.0188 *
## container:time 0.0469042 0.0293172 1.600 0.1117
## container:I(time^2) -0.0002283 0.0003461 -0.660 0.5106
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.008 on 149 degrees of freedom
## Multiple R-squared: 0.5186, Adjusted R-squared: 0.4831
## F-statistic: 14.59 on 11 and 149 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = rdt_poly_sfw, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.69124 -0.24652 -0.06983 0.18138 2.25175
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -7.004e-01 4.129e-01 -1.696 0.0919 .
## container 1.862e-01 2.124e-01 0.877 0.3821
## time -1.498e-02 7.596e-03 -1.971 0.0505 .
## I(time^2) -1.467e-04 8.237e-05 -1.781 0.0770 .
## temp_c -4.899e-03 5.210e-03 -0.940 0.3486
## humi_p 2.446e-03 3.830e-03 0.639 0.5240
## prcp_mm -2.077e-02 1.688e-02 -1.230 0.2206
## liquors 1.013e-02 2.082e-02 0.487 0.6272
## sales 1.249e-03 2.080e-04 6.005 1.4e-08 ***
## halfs 1.095e-02 1.207e-02 0.907 0.3658
## container:time 2.138e-02 1.195e-02 1.788 0.0758 .
## container:I(time^2) 5.136e-05 1.411e-04 0.364 0.7164
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4112 on 149 degrees of freedom
## Multiple R-squared: 0.3679, Adjusted R-squared: 0.3212
## F-statistic: 7.884 on 11 and 149 DF, p-value: 1.063e-10##
## Call:
## lm(formula = rdt_poly_lfw, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.53737 -0.42153 -0.08896 0.35757 1.87042
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.7668065 0.7103879 -2.487 0.01398 *
## container 0.1976864 0.3654045 0.541 0.58931
## time -0.0039315 0.0130699 -0.301 0.76398
## I(time^2) 0.0000137 0.0001417 0.097 0.92311
## temp_c -0.0034488 0.0089637 -0.385 0.70097
## humi_p 0.0078720 0.0065890 1.195 0.23410
## prcp_mm -0.0305946 0.0290477 -1.053 0.29393
## liquors -0.0169643 0.0358244 -0.474 0.63652
## sales 0.0028854 0.0003579 8.061 2.27e-13 ***
## halfs 0.0593525 0.0207728 2.857 0.00489 **
## container:time 0.0255287 0.0205679 1.241 0.21649
## container:I(time^2) -0.0002796 0.0002428 -1.152 0.25130
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7074 on 149 degrees of freedom
## Multiple R-squared: 0.5297, Adjusted R-squared: 0.495
## F-statistic: 15.26 on 11 and 149 DF, p-value: < 2.2e-16Ass-Poly
- Linearity of the relationships between the dependent and independent variables
- Normality of the residuals
- Homoscedasticity of the residuals
- No influential points (outliers)
- No multicollinearity
- Independence of the observations
## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.013).## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.003).## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.007).## Warning: Non-normality of residuals detected (p < .001).## Warning: Non-normality of residuals detected (p < .001).## Warning: Non-normality of residuals detected (p = 0.013).##
## studentized Breusch-Pagan test
##
## data: rdt_poly_fw
## BP = 16.435, df = 11, p-value = 0.1257##
## studentized Breusch-Pagan test
##
## data: rdt_poly_sfw
## BP = 11.26, df = 11, p-value = 0.4218##
## studentized Breusch-Pagan test
##
## data: rdt_poly_lfw
## BP = 16.008, df = 11, p-value = 0.1408## OK: Residuals appear to be independent and not autocorrelated (p = 0.448).## OK: Residuals appear to be independent and not autocorrelated (p = 0.618).## OK: Residuals appear to be independent and not autocorrelated (p = 0.484).
Per Customer
Interaction
##
## Call:
## lm(formula = rdt_int_fw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.085830 -0.026913 -0.000256 0.022668 0.144070
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0634025 0.0084860 7.471 5.19e-12 ***
## container 0.0205965 0.0123107 1.673 0.0963 .
## time -0.0002550 0.0001694 -1.505 0.1344
## container:time 0.0002948 0.0002683 1.099 0.2736
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03901 on 157 degrees of freedom
## Multiple R-squared: 0.03369, Adjusted R-squared: 0.01523
## F-statistic: 1.825 on 3 and 157 DF, p-value: 0.1449##
## Call:
## lm(formula = rdt_int_sfw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.025637 -0.009649 -0.001998 0.007429 0.107324
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.413e-02 3.438e-03 7.018 6.35e-11 ***
## container 6.087e-04 4.988e-03 0.122 0.903
## time -6.278e-05 6.865e-05 -0.914 0.362
## container:time 7.849e-05 1.087e-04 0.722 0.471
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0158 on 157 degrees of freedom
## Multiple R-squared: 0.00791, Adjusted R-squared: -0.01105
## F-statistic: 0.4173 on 3 and 157 DF, p-value: 0.7408##
## Call:
## lm(formula = rdt_int_lfw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.060368 -0.021770 0.000354 0.019225 0.067531
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0392726 0.0060700 6.470 1.19e-09 ***
## container 0.0199878 0.0088058 2.270 0.0246 *
## time -0.0001922 0.0001212 -1.586 0.1148
## container:time 0.0002163 0.0001919 1.127 0.2615
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.0279 on 157 degrees of freedom
## Multiple R-squared: 0.06328, Adjusted R-squared: 0.04538
## F-statistic: 3.535 on 3 and 157 DF, p-value: 0.01621Ass-Interaction
- Linearity of the relationships between the dependent and independent variables
- Normality of the residuals
- Homoscedasticity of the residuals
- No influential points (outliers)
- No multicollinearity
- Independence of the observations
## OK: Error variance appears to be homoscedastic (p = 0.560).## OK: Error variance appears to be homoscedastic (p = 0.085).## OK: Error variance appears to be homoscedastic (p = 0.357).## OK: residuals appear as normally distributed (p = 0.310).## Warning: Non-normality of residuals detected (p < .001).## OK: residuals appear as normally distributed (p = 0.506).##
## studentized Breusch-Pagan test
##
## data: rdt_int_fw_p
## BP = 0.39927, df = 3, p-value = 0.9404##
## studentized Breusch-Pagan test
##
## data: rdt_int_sfw_p
## BP = 0.78557, df = 3, p-value = 0.8529##
## studentized Breusch-Pagan test
##
## data: rdt_int_lfw_p
## BP = 1.5608, df = 3, p-value = 0.6683## OK: Residuals appear to be independent and not autocorrelated (p = 0.636).## OK: Residuals appear to be independent and not autocorrelated (p = 0.838).## OK: Residuals appear to be independent and not autocorrelated (p = 0.604).
Multiple model
##
## Call:
## lm(formula = rdt_multi_fw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.074837 -0.024496 -0.002514 0.019536 0.148986
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.272e-02 3.556e-02 0.639 0.5239
## container 2.445e-02 1.382e-02 1.768 0.0790 .
## time -2.128e-04 2.480e-04 -0.858 0.3921
## temp_c -1.980e-04 4.767e-04 -0.415 0.6785
## humi_p 9.816e-05 3.502e-04 0.280 0.7796
## prcp_mm -1.753e-03 1.524e-03 -1.150 0.2519
## liquors 1.114e-03 1.918e-03 0.581 0.5624
## sales 4.082e-05 1.911e-05 2.135 0.0343 *
## halfs 7.092e-04 1.107e-03 0.641 0.5227
## container:time 1.984e-04 3.784e-04 0.524 0.6008
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03793 on 151 degrees of freedom
## Multiple R-squared: 0.1212, Adjusted R-squared: 0.06883
## F-statistic: 2.314 on 9 and 151 DF, p-value: 0.01819##
## Call:
## lm(formula = rdt_multi_sfw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.027494 -0.010028 -0.001538 0.007102 0.104802
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.945e-02 1.477e-02 1.317 0.190
## container 4.123e-03 5.743e-03 0.718 0.474
## time -7.996e-05 1.030e-04 -0.776 0.439
## temp_c -1.554e-04 1.980e-04 -0.785 0.434
## humi_p -3.292e-05 1.455e-04 -0.226 0.821
## prcp_mm -7.440e-04 6.329e-04 -1.175 0.242
## liquors 6.531e-04 7.967e-04 0.820 0.414
## sales 9.221e-06 7.940e-06 1.161 0.247
## halfs -2.701e-04 4.599e-04 -0.587 0.558
## container:time 4.472e-05 1.572e-04 0.285 0.776
##
## Residual standard error: 0.01576 on 151 degrees of freedom
## Multiple R-squared: 0.05157, Adjusted R-squared: -0.00496
## F-statistic: 0.9123 on 9 and 151 DF, p-value: 0.5163##
## Call:
## lm(formula = rdt_multi_lfw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.051511 -0.017780 -0.004288 0.016169 0.078517
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.269e-03 2.512e-02 0.130 0.8966
## container 2.032e-02 9.764e-03 2.081 0.0391 *
## time -1.329e-04 1.752e-04 -0.759 0.4493
## temp_c -4.256e-05 3.367e-04 -0.126 0.8996
## humi_p 1.311e-04 2.474e-04 0.530 0.5969
## prcp_mm -1.009e-03 1.076e-03 -0.937 0.3502
## liquors 4.605e-04 1.355e-03 0.340 0.7344
## sales 3.160e-05 1.350e-05 2.340 0.0206 *
## halfs 9.793e-04 7.819e-04 1.252 0.2124
## container:time 1.537e-04 2.673e-04 0.575 0.5661
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02679 on 151 degrees of freedom
## Multiple R-squared: 0.1694, Adjusted R-squared: 0.1198
## F-statistic: 3.421 on 9 and 151 DF, p-value: 0.0007411Ass-Multiple
- Linearity of the relationships between the dependent and independent variables
- Normality of the residuals
- Homoscedasticity of the residuals
- No influential points (outliers)
- No multicollinearity
- Independence of the observations
## OK: Error variance appears to be homoscedastic (p = 0.077).## OK: Error variance appears to be homoscedastic (p = 0.053).## OK: Error variance appears to be homoscedastic (p = 0.334).## Warning: Non-normality of residuals detected (p = 0.001).## Warning: Non-normality of residuals detected (p < .001).## Warning: Non-normality of residuals detected (p = 0.023).##
## studentized Breusch-Pagan test
##
## data: rdt_multi_fw_p
## BP = 15.097, df = 9, p-value = 0.08831##
## studentized Breusch-Pagan test
##
## data: rdt_multi_sfw_p
## BP = 10.355, df = 9, p-value = 0.3225##
## studentized Breusch-Pagan test
##
## data: rdt_multi_lfw_p
## BP = 13.732, df = 9, p-value = 0.1322## OK: Residuals appear to be independent and not autocorrelated (p = 0.894).## OK: Residuals appear to be independent and not autocorrelated (p = 0.794).## OK: Residuals appear to be independent and not autocorrelated (p = 0.890).
polynomial model
##
## Call:
## lm(formula = rdt_poly_fw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.07797 -0.02446 -0.00292 0.02073 0.14856
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.857e-02 3.821e-02 0.486 0.6277
## container 1.680e-02 1.965e-02 0.855 0.3940
## time -3.906e-04 7.030e-04 -0.556 0.5793
## I(time^2) -2.359e-06 7.623e-06 -0.309 0.7574
## temp_c -1.356e-04 4.821e-04 -0.281 0.7789
## humi_p 1.238e-04 3.544e-04 0.349 0.7273
## prcp_mm -2.078e-03 1.562e-03 -1.330 0.1855
## liquors 1.201e-03 1.927e-03 0.623 0.5339
## sales 4.164e-05 1.925e-05 2.163 0.0321 *
## halfs 6.986e-04 1.117e-03 0.625 0.5327
## container:time 1.170e-03 1.106e-03 1.058 0.2919
## container:I(time^2) -8.306e-06 1.306e-05 -0.636 0.5257
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03805 on 149 degrees of freedom
## Multiple R-squared: 0.1274, Adjusted R-squared: 0.06295
## F-statistic: 1.977 on 11 and 149 DF, p-value: 0.0344##
## Call:
## lm(formula = rdt_poly_sfw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.027962 -0.010345 -0.002081 0.006764 0.102708
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.199e-02 1.582e-02 0.758 0.450
## container 6.501e-03 8.136e-03 0.799 0.426
## time -4.329e-04 2.910e-04 -1.487 0.139
## I(time^2) -4.166e-06 3.156e-06 -1.320 0.189
## temp_c -1.347e-04 1.996e-04 -0.675 0.501
## humi_p -5.413e-06 1.467e-04 -0.037 0.971
## prcp_mm -8.951e-04 6.468e-04 -1.384 0.168
## liquors 7.133e-04 7.977e-04 0.894 0.373
## sales 1.022e-05 7.970e-06 1.282 0.202
## halfs -3.289e-04 4.625e-04 -0.711 0.478
## container:time 6.071e-04 4.580e-04 1.326 0.187
## container:I(time^2) 1.443e-06 5.406e-06 0.267 0.790
##
## Residual standard error: 0.01575 on 149 degrees of freedom
## Multiple R-squared: 0.06457, Adjusted R-squared: -0.004489
## F-statistic: 0.935 on 11 and 149 DF, p-value: 0.5087##
## Call:
## lm(formula = rdt_poly_lfw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.050007 -0.018305 -0.003888 0.017097 0.076798
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.582e-03 2.697e-02 0.244 0.8076
## container 1.030e-02 1.387e-02 0.742 0.4590
## time 4.226e-05 4.962e-04 0.085 0.9322
## I(time^2) 1.808e-06 5.381e-06 0.336 0.7374
## temp_c -8.461e-07 3.403e-04 -0.002 0.9980
## humi_p 1.292e-04 2.502e-04 0.517 0.6062
## prcp_mm -1.183e-03 1.103e-03 -1.073 0.2851
## liquors 4.880e-04 1.360e-03 0.359 0.7203
## sales 3.143e-05 1.359e-05 2.313 0.0221 *
## halfs 1.028e-03 7.887e-04 1.303 0.1947
## container:time 5.629e-04 7.809e-04 0.721 0.4721
## container:I(time^2) -9.749e-06 9.218e-06 -1.058 0.2920
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02686 on 149 degrees of freedom
## Multiple R-squared: 0.1761, Adjusted R-squared: 0.1152
## F-statistic: 2.895 on 11 and 149 DF, p-value: 0.00176Ass-Poly
- Linearity of the relationships between the dependent and independent variables
- Normality of the residuals
- Homoscedasticity of the residuals
- No influential points (outliers)
- No multicollinearity
- Independence of the observations
## OK: Error variance appears to be homoscedastic (p = 0.107).## Warning: Heteroscedasticity (non-constant error variance) detected (p = 0.004).## OK: Error variance appears to be homoscedastic (p = 0.321).## Warning: Non-normality of residuals detected (p = 0.012).## Warning: Non-normality of residuals detected (p < .001).## Warning: Non-normality of residuals detected (p = 0.023).##
## studentized Breusch-Pagan test
##
## data: rdt_poly_fw_p
## BP = 17.523, df = 11, p-value = 0.09332##
## studentized Breusch-Pagan test
##
## data: rdt_poly_sfw_p
## BP = 11.556, df = 11, p-value = 0.3979##
## studentized Breusch-Pagan test
##
## data: rdt_poly_lfw_p
## BP = 16.922, df = 11, p-value = 0.1102## OK: Residuals appear to be independent and not autocorrelated (p = 0.994).## OK: Residuals appear to be independent and not autocorrelated (p = 0.850).## OK: Residuals appear to be independent and not autocorrelated (p = 0.886).
Cubic model
##
## Call:
## lm(formula = rdt_poly3_fw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.075327 -0.024795 -0.003087 0.023996 0.150164
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.343e-03 3.869e-02 0.164 0.8700
## container 3.233e-02 2.412e-02 1.340 0.1823
## time -3.297e-03 1.750e-03 -1.885 0.0615 .
## I(time^2) -8.808e-05 4.813e-05 -1.830 0.0693 .
## I(time^3) -6.576e-07 3.644e-07 -1.805 0.0732 .
## temp_c 8.336e-05 5.189e-04 0.161 0.8726
## humi_p 6.240e-05 3.559e-04 0.175 0.8610
## prcp_mm -2.544e-03 1.577e-03 -1.613 0.1089
## liquors 8.443e-04 1.928e-03 0.438 0.6621
## sales 4.040e-05 1.920e-05 2.105 0.0370 *
## halfs 9.267e-04 1.120e-03 0.827 0.4093
## container:time 4.590e-03 2.677e-03 1.714 0.0886 .
## container:I(time^2) 6.111e-05 8.238e-05 0.742 0.4593
## container:I(time^3) 7.933e-07 6.624e-07 1.198 0.2330
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03787 on 147 degrees of freedom
## Multiple R-squared: 0.147, Adjusted R-squared: 0.07153
## F-statistic: 1.948 on 13 and 147 DF, p-value: 0.02915##
## Call:
## lm(formula = rdt_poly3_sfw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.028116 -0.010438 -0.001034 0.006871 0.103441
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.987e-03 1.601e-02 0.436 0.6632
## container 1.338e-02 9.986e-03 1.340 0.1822
## time -1.653e-03 7.242e-04 -2.282 0.0239 *
## I(time^2) -4.020e-05 1.992e-05 -2.018 0.0454 *
## I(time^3) -2.764e-07 1.508e-07 -1.832 0.0690 .
## temp_c -3.778e-05 2.148e-04 -0.176 0.8606
## humi_p -3.221e-05 1.473e-04 -0.219 0.8272
## prcp_mm -1.087e-03 6.528e-04 -1.664 0.0981 .
## liquors 5.660e-04 7.981e-04 0.709 0.4793
## sales 9.731e-06 7.946e-06 1.225 0.2226
## halfs -2.356e-04 4.636e-04 -0.508 0.6121
## container:time 1.973e-03 1.108e-03 1.780 0.0771 .
## container:I(time^2) 3.300e-05 3.410e-05 0.968 0.3347
## container:I(time^3) 3.118e-07 2.742e-07 1.137 0.2573
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01568 on 147 degrees of freedom
## Multiple R-squared: 0.08587, Adjusted R-squared: 0.005027
## F-statistic: 1.062 on 13 and 147 DF, p-value: 0.3965##
## Call:
## lm(formula = rdt_poly3_lfw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.050013 -0.019310 -0.003956 0.016136 0.074786
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.442e-04 2.741e-02 -0.024 0.9813
## container 1.895e-02 1.709e-02 1.108 0.2695
## time -1.644e-03 1.240e-03 -1.327 0.1867
## I(time^2) -4.788e-05 3.410e-05 -1.404 0.1623
## I(time^3) -3.813e-07 2.582e-07 -1.477 0.1419
## temp_c 1.211e-04 3.676e-04 0.330 0.7422
## humi_p 9.461e-05 2.521e-04 0.375 0.7080
## prcp_mm -1.457e-03 1.117e-03 -1.304 0.1942
## liquors 2.783e-04 1.366e-03 0.204 0.8389
## sales 3.067e-05 1.360e-05 2.255 0.0256 *
## halfs 1.162e-03 7.935e-04 1.465 0.1451
## container:time 2.617e-03 1.897e-03 1.380 0.1698
## container:I(time^2) 2.811e-05 5.836e-05 0.482 0.6308
## container:I(time^3) 4.815e-07 4.693e-07 1.026 0.3066
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02683 on 147 degrees of freedom
## Multiple R-squared: 0.1887, Adjusted R-squared: 0.117
## F-statistic: 2.631 on 13 and 147 DF, p-value: 0.002514Quartic model
##
## Call:
## lm(formula = rdt_poly4_fw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.075470 -0.024339 -0.003301 0.023904 0.148010
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.489e-02 4.337e-02 0.343 0.7318
## container 2.588e-02 3.012e-02 0.859 0.3916
## time -1.926e-03 3.541e-03 -0.544 0.5873
## I(time^2) -1.803e-05 1.643e-04 -0.110 0.9128
## I(time^3) 5.983e-07 2.839e-06 0.211 0.8334
## I(time^4) 7.256e-09 1.627e-08 0.446 0.6562
## temp_c 9.970e-05 5.242e-04 0.190 0.8494
## humi_p 3.479e-05 3.634e-04 0.096 0.9239
## prcp_mm -2.586e-03 1.593e-03 -1.623 0.1068
## liquors 8.721e-04 1.946e-03 0.448 0.6547
## sales 4.080e-05 1.934e-05 2.109 0.0366 *
## halfs 9.161e-04 1.127e-03 0.813 0.4178
## container:time 3.297e-03 5.307e-03 0.621 0.5354
## container:I(time^2) -1.457e-05 2.720e-04 -0.054 0.9573
## container:I(time^3) -3.401e-07 5.263e-06 -0.065 0.9486
## container:I(time^4) -8.117e-09 3.353e-08 -0.242 0.8091
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03811 on 145 degrees of freedom
## Multiple R-squared: 0.1481, Adjusted R-squared: 0.06002
## F-statistic: 1.681 on 15 and 145 DF, p-value: 0.0607##
## Call:
## lm(formula = rdt_poly4_sfw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.026376 -0.010198 -0.001428 0.006948 0.100389
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.889e-02 1.779e-02 1.062 0.2899
## container 1.075e-03 1.235e-02 0.087 0.9307
## time 2.333e-04 1.452e-03 0.161 0.8726
## I(time^2) 5.598e-05 6.736e-05 0.831 0.4073
## I(time^3) 1.445e-06 1.164e-06 1.241 0.2166
## I(time^4) 9.930e-09 6.670e-09 1.489 0.1387
## temp_c -2.364e-05 2.150e-04 -0.110 0.9126
## humi_p -7.340e-05 1.490e-04 -0.493 0.6231
## prcp_mm -1.114e-03 6.533e-04 -1.705 0.0904 .
## liquors 5.647e-04 7.979e-04 0.708 0.4803
## sales 1.042e-05 7.931e-06 1.313 0.1911
## halfs -2.575e-04 4.623e-04 -0.557 0.5785
## container:time 1.206e-03 2.176e-03 0.554 0.5803
## container:I(time^2) -1.334e-04 1.115e-04 -1.196 0.2335
## container:I(time^3) 7.772e-08 2.158e-06 0.036 0.9713
## container:I(time^4) -2.000e-08 1.375e-08 -1.455 0.1479
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01563 on 145 degrees of freedom
## Multiple R-squared: 0.104, Adjusted R-squared: 0.01131
## F-statistic: 1.122 on 15 and 145 DF, p-value: 0.3418##
## Call:
## lm(formula = rdt_poly4_lfw_p, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.04932 -0.01875 -0.00414 0.01605 0.07566
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -4.000e-03 3.072e-02 -0.130 0.8966
## container 2.480e-02 2.133e-02 1.163 0.2469
## time -2.159e-03 2.508e-03 -0.861 0.3907
## I(time^2) -7.401e-05 1.164e-04 -0.636 0.5257
## I(time^3) -8.463e-07 2.011e-06 -0.421 0.6745
## I(time^4) -2.674e-09 1.152e-08 -0.232 0.8168
## temp_c 1.233e-04 3.713e-04 0.332 0.7403
## humi_p 1.082e-04 2.574e-04 0.420 0.6749
## prcp_mm -1.472e-03 1.129e-03 -1.304 0.1942
## liquors 3.074e-04 1.378e-03 0.223 0.8238
## sales 3.038e-05 1.370e-05 2.218 0.0281 *
## halfs 1.174e-03 7.986e-04 1.470 0.1438
## container:time 2.091e-03 3.760e-03 0.556 0.5789
## container:I(time^2) 1.189e-04 1.927e-04 0.617 0.5383
## container:I(time^3) -4.178e-07 3.728e-06 -0.112 0.9109
## container:I(time^4) 1.189e-08 2.375e-08 0.500 0.6175
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02699 on 145 degrees of freedom
## Multiple R-squared: 0.1901, Adjusted R-squared: 0.1064
## F-statistic: 2.269 on 15 and 145 DF, p-value: 0.006618Some model
##
## Call:
## lm(formula = rdt_sales, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -464.65 -156.75 -7.94 132.75 452.58
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 653.2167 45.3342 14.409 <2e-16 ***
## container -21.1864 65.7665 -0.322 0.7478
## time -2.1632 0.9051 -2.390 0.0180 *
## container:time 3.0966 1.4334 2.160 0.0323 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 208.4 on 157 degrees of freedom
## Multiple R-squared: 0.07338, Adjusted R-squared: 0.05568
## F-statistic: 4.145 on 3 and 157 DF, p-value: 0.00737##
## Call:
## lm(formula = rdt_sales_mult, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -400.38 -104.13 -9.09 93.36 439.38
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 382.140 147.670 2.588 0.0106 *
## container -31.487 58.605 -0.537 0.5919
## time -1.011 1.049 -0.964 0.3367
## temp_c 2.704 2.011 1.345 0.1807
## humi_p 1.429 1.481 0.965 0.3362
## prcp_mm -5.455 6.451 -0.846 0.3991
## liquors 43.158 7.347 5.874 2.59e-08 ***
## halfs 28.934 4.069 7.110 4.23e-11 ***
## container:time 1.546 1.601 0.966 0.3357
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 160.9 on 152 degrees of freedom
## Multiple R-squared: 0.4648, Adjusted R-squared: 0.4366
## F-statistic: 16.5 on 8 and 152 DF, p-value: < 2.2e-16##
## Call:
## lm(formula = rdt_sales, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -398.79 -101.98 -7.22 94.60 437.60
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 441.27206 157.99058 2.793 0.0059 **
## container -63.00940 83.19361 -0.757 0.4500
## time 1.96129 2.97708 0.659 0.5110
## I(time^2) 0.03465 0.03220 1.076 0.2837
## temp_c 2.57848 2.03385 1.268 0.2068
## humi_p 1.20252 1.49982 0.802 0.4239
## prcp_mm -4.47457 6.61600 -0.676 0.4999
## liquors 42.38676 7.40288 5.726 5.44e-08 ***
## halfs 29.22421 4.09386 7.139 3.77e-11 ***
## container:time -2.27212 4.68807 -0.485 0.6286
## container:I(time^2) -0.02417 0.05535 -0.437 0.6630
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 161.4 on 150 degrees of freedom
## Multiple R-squared: 0.4691, Adjusted R-squared: 0.4337
## F-statistic: 13.25 on 10 and 150 DF, p-value: < 2.2e-16Local Regression
per Customer
##
## Call:
## lm(formula = food_waste_p_kg ~ container, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.071951 -0.021391 0.001999 0.021733 0.079921
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.066985 0.007257 9.230 2.69e-12 ***
## container 0.016731 0.010164 1.646 0.106
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03629 on 49 degrees of freedom
## Multiple R-squared: 0.0524, Adjusted R-squared: 0.03306
## F-statistic: 2.709 on 1 and 49 DF, p-value: 0.1062##
## Call:
## lm(formula = solid_waste_p_kg ~ container, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.022725 -0.006960 -0.002115 0.007308 0.025352
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.022725 0.002242 10.135 1.29e-13 ***
## container 0.001804 0.003140 0.575 0.568
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01121 on 49 degrees of freedom
## Multiple R-squared: 0.006691, Adjusted R-squared: -0.01358
## F-statistic: 0.3301 on 1 and 49 DF, p-value: 0.5682##
## Call:
## lm(formula = liquid_waste_p_kg ~ container, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.056246 -0.019655 0.000813 0.019476 0.068086
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.044261 0.005547 7.979 2.06e-10 ***
## container 0.014926 0.007769 1.921 0.0605 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02774 on 49 degrees of freedom
## Multiple R-squared: 0.07005, Adjusted R-squared: 0.05107
## F-statistic: 3.691 on 1 and 49 DF, p-value: 0.06053Interaction
##
## Call:
## lm(formula = food_waste_p_kg ~ container * time, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.076915 -0.019486 -0.000832 0.025310 0.076839
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0552496 0.0151211 3.654 0.000649 ***
## container 0.0233299 0.0205930 1.133 0.263003
## time -0.0009027 0.0010172 -0.888 0.379327
## container:time 0.0013136 0.0013979 0.940 0.352184
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03667 on 47 degrees of freedom
## Multiple R-squared: 0.07158, Adjusted R-squared: 0.01232
## F-statistic: 1.208 on 3 and 47 DF, p-value: 0.3172##
## Call:
## lm(formula = solid_waste_p_kg ~ container * time, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.025961 -0.006713 -0.002136 0.008028 0.024176
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0189002 0.0046765 4.042 0.000195 ***
## container 0.0054568 0.0063688 0.857 0.395900
## time -0.0002942 0.0003146 -0.935 0.354488
## container:time 0.0003079 0.0004323 0.712 0.479863
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01134 on 47 degrees of freedom
## Multiple R-squared: 0.02488, Adjusted R-squared: -0.03736
## F-statistic: 0.3997 on 3 and 47 DF, p-value: 0.7538##
## Call:
## lm(formula = liquid_waste_p_kg ~ container * time, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.059985 -0.016844 0.000476 0.019769 0.065107
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0363494 0.0115661 3.143 0.0029 **
## container 0.0178730 0.0157515 1.135 0.2623
## time -0.0006086 0.0007780 -0.782 0.4380
## container:time 0.0010057 0.0010693 0.941 0.3517
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02805 on 47 degrees of freedom
## Multiple R-squared: 0.08762, Adjusted R-squared: 0.02938
## F-statistic: 1.504 on 3 and 47 DF, p-value: 0.2256
Multiple
##
## Call:
## lm(formula = food_waste_p_kg ~ container * time + temp_c + humi_p +
## prcp_mm + liquors + sales + halfs, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.070198 -0.018478 -0.000523 0.021209 0.070930
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.963e-02 7.727e-02 1.031 0.309
## container 1.269e-02 2.150e-02 0.590 0.558
## time -7.400e-04 1.049e-03 -0.706 0.484
## temp_c 1.008e-03 8.579e-04 1.174 0.247
## humi_p -4.189e-04 8.007e-04 -0.523 0.604
## prcp_mm -3.606e-03 3.060e-03 -1.178 0.245
## liquors 8.516e-04 3.177e-03 0.268 0.790
## sales 3.606e-05 3.459e-05 1.043 0.303
## halfs 3.668e-04 2.245e-03 0.163 0.871
## container:time 1.555e-03 1.585e-03 0.981 0.332
##
## Residual standard error: 0.03567 on 41 degrees of freedom
## Multiple R-squared: 0.2336, Adjusted R-squared: 0.06541
## F-statistic: 1.389 on 9 and 41 DF, p-value: 0.2247##
## Call:
## lm(formula = solid_waste_p_kg ~ container * time + temp_c + humi_p +
## prcp_mm + liquors + sales + halfs, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.0186022 -0.0056049 -0.0005597 0.0058769 0.0210676
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.528e-02 2.293e-02 1.539 0.1315
## container 1.389e-03 6.381e-03 0.218 0.8288
## time -2.229e-04 3.112e-04 -0.716 0.4778
## temp_c 5.332e-04 2.546e-04 2.095 0.0424 *
## humi_p -2.283e-04 2.376e-04 -0.961 0.3421
## prcp_mm -8.376e-04 9.079e-04 -0.923 0.3616
## liquors 1.705e-04 9.426e-04 0.181 0.8573
## sales 1.810e-05 1.026e-05 1.763 0.0853 .
## halfs -4.264e-04 6.661e-04 -0.640 0.5257
## container:time 3.030e-04 4.703e-04 0.644 0.5230
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01058 on 41 degrees of freedom
## Multiple R-squared: 0.2592, Adjusted R-squared: 0.09653
## F-statistic: 1.594 on 9 and 41 DF, p-value: 0.1495##
## Call:
## lm(formula = liquid_waste_p_kg ~ container * time + temp_c +
## humi_p + prcp_mm + liquors + sales + halfs, data = .)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.051596 -0.015189 -0.001578 0.016023 0.063417
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.436e-02 6.054e-02 0.733 0.468
## container 1.130e-02 1.685e-02 0.671 0.506
## time -5.171e-04 8.218e-04 -0.629 0.533
## temp_c 4.743e-04 6.722e-04 0.706 0.484
## humi_p -1.905e-04 6.274e-04 -0.304 0.763
## prcp_mm -2.768e-03 2.398e-03 -1.155 0.255
## liquors 6.810e-04 2.489e-03 0.274 0.786
## sales 1.797e-05 2.710e-05 0.663 0.511
## halfs 7.931e-04 1.759e-03 0.451 0.654
## container:time 1.252e-03 1.242e-03 1.008 0.319
##
## Residual standard error: 0.02795 on 41 degrees of freedom
## Multiple R-squared: 0.2097, Adjusted R-squared: 0.03621
## F-statistic: 1.209 on 9 and 41 DF, p-value: 0.3161
